Divisors of 4 (numbers that you can divide four by and get a whole number): 2, 1, 4 (i.e. 2x2, 1x4, 4x1... again... the first number that is non-prime... 1x1, 1x2, 1x3, 1x5).. it only has one other divisor (compared to the next non-prime 6: 1,2,3,6 (2x3, 1x6))

I think of the tetrahedron branching off in two directions with two each as a really powerful example of the 2x2, 2^2 and the beginning of the third dimension... like a flat square/plane popping and twisting into a whole, 3D object.... or like folding a square-ish shape in half on the diagonal and connecting the free corners with a line...
Maybe you can imagine something like this:http://www.cc.gatech.edu/~mluffel/20...ges/tetra0.png

It's interesting that no matter what orientation you put the points of a triangle in, it is still flat... Try it out!